Magnetic Field

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In physics, the magnetism field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles. Magnetic fields surround electric currents, magnetic dipoles, and changing electric fields.

When placed in a magnetic field, magnetic dipoles align their axes to be parallel with the field lines, as can be seen when iron filings are in the presence of a magnet. Magnetic fields also have their own energy and momentum, with an energy density proportional to the square of the field intensity. The magnetic field is measured in the units of Tesla (unit) (SI units) or gauss (unit) (cgs units).

There are some notable specific incarnations of the magnetic field. For the physics of magnetic materials, see magnetism and magnet, and more specifically ferromagnetism, paramagnetism, and diamagnetism. For constant magnetic fields, such as are generated by stationary dipoles and steady currents, see magnetostatics. For magnetic fields created by changing electric fields, see electromagnetism.

The electric field and the magnetic field are components of the electromagnetic field.

Definition In classical physics, the magnetic field \mathbf{B} is a vector field (that is, some vector at every point of space and time), with SI units of Tesla (unit) (one Tesla is one newton-second per coulomb-metre) and cgs units of gauss (unit). As a vector field, it has the property of being solenoidal.

The field \mathbf{B} can be both defined and measured by means of a small magnetic dipole (i.e., magnet). The magnetic field exerts a torque on magnetic dipoles that tends to make them point in the same direction as the magnetic field (as in a compass), and moreover the magnitude of that torque is proportional to the magnitude of the magnetic field. Therefore, in order to measure the magnetic field at a particular point in space, you can put a small freely-rotating bar magnet (such as a compass) there: the direction it winds up pointing is the direction of \mathbf{B}; and the ratio of the maximum magnitude of the torque to the dipole moment of the bar magnet is the magnitude ] law (see below), or as the solution to Maxwell's equations.)

It follows from any of these definitions that the magnetic field vector (being a vector product) is a pseudovector (also called an axial vector).

B and H There are two quantities that physicists may refer to as the magnetic field, notated \mathbf{H} and \mathbf{B}. The vector field \mathbf{H}is known among electrical engineers as the magnetic field intensity or magnetic field strength also known as auxiliary magnetic field or magnetizing field. The vector field \mathbf{B} is known as magnetic flux density or magnetic induction or simply magnetic field, as used by physicists, and has the SI units of Tesla (unit) (T), equivalent to weber (unit) (Wb) per square metre or volt second per square metre. Magnetic flux has the SI units of webers so the \mathbf{B} field is that of its areal density. Magnetic Field Strength is also sometimes called Magnetic Field Intensity. For more information reference the sources Durney and Johnson, and also Rao. The vector field \mathbf{H} has the SI units of amperes per metre and is something of the magnetic analog to the electric displacement field represented by \mathbf{D}, with the SI units of the latter being ampere-seconds per square metre. Although the term "magnetic field" was historically reserved for \mathbf{H}, with \mathbf{B} being termed the "magnetic induction", \mathbf{B} is now understood to be the more fundamental entity, and most modern writers refer to \mathbf{B} as the magnetic field, except when context fails to make it clear whether the quantity being discussed is \mathbf{H} or \mathbf{B}. See: The standard graduate textbook by Jackson follows this usage. Edward Purcell, in Electricity and Magnetism, McGraw-Hill, 1963, writes, Even some modern writers who treat B as the primary field feel obliged to call it the magnetic induction because the name magnetic field was historically preempted by H. This seems clumsy and pedantic. If you go into the laboratory and ask a physicist what causes the pion trajectories in his bubble chamber to curve, he'll probably answer "magnetic field," not "magnetic induction." You will seldom hear a geophysicist refer to the earth's magnetic induction, or an astrophysicist talk about the magnetic induction of the galaxy. We propose to keep on calling B the magnetic field. As for H, although other names have been invented for it, we shall call it "the field H" or even "the magnetic field H".

The difference between the \mathbf{B} and the \mathbf{H} vectors can be traced back to Maxwell's 1855 paper entitled On Faraday's Lines of Force. It is later clarified in his concept of a sea of molecular vortices that appears in his 1861 paper On Physical Lines of Force - 1861. Within that context, \mathbf{H} represented pure vorticity (spin), whereas \mathbf{B} was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered magnetic permeability µ to be a measure of the density of the vortex sea. Hence the relationship,

(1) Magnetic induction current causes a magnetic current density

\mathbf{B} = \mu \mathbf{H}

was essentially a rotational analogy to the linear electric current relationship,

(2) Electric convection current

\mathbf{J} = \rho \mathbf{v}

where \rho is electric charge density. \mathbf{B} was seen as a kind of magnetic current of vortices aligned in their axial planes, with \mathbf{H} being the circumferential velocity of the vortices. With µ representing vortex density, we can now see how the product of µ with vorticity \mathbf{H} leads to the term magnetic flux density which we denote as \mathbf{B}.

The electric current equation can be viewed as a convective current of electric charge that involves linear motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the \mathbf{B} vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse square law force.

The extension of the above considerations confirms that where \mathbf{B} is to \mathbf{H}, and where \mathbf{J} is to ρ, then it necessarily follows from Gauss's law and from the equation of continuity of charge that \mathbf{E} is to \mathbf{D}. Ie. \mathbf{B} parallels with \mathbf{E}, whereas \mathbf{H} parallels with \mathbf{D}.

In SI units, \mathbf{B} \ and \mathbf{H} \ are measured in Tesla (unit)s (T) and amperes per metre (A/m), respectively; or, in cgs units, in Gauss (unit) (G) and oersteds (Oe), respectively. Two parallel wires carrying an electric current in the same direction will generate a magnetic field that will cause a force of attraction between them. This fact is used to define the value of an ampere of electric current.

The fields \mathbf{B} and \mathbf{H} are also related by the equation \mathbf{B}=\mu_0(\mathbf{H}+\mathbf{M}) (SI units) \mathbf{B}=\mathbf{H}+4\pi\mathbf{M} (cgs units), where \mathbf{M} is magnetization.

Force due to a magnetic field Force on a charged particle \mathbf{F} = q (\mathbf{v} \times \mathbf{B}),

where F is the force (in newtons) q is the electric charge of the particle (in coulombs) v is the instantaneous velocity of the particle (in meters per second) and × is the cross product.

Force on wire segment Integrating the Lorentz force on an individual charged particle over a flow (current) of charged particles results in the Lorentz force on a stationary wire carrying electric current: \mathbf{F} = I \cdot \mathbf{l} \times \mathbf{B} \,

where F = forces, measured in newtons I = current in wire, measured in amperes B = magnetic field, measured in teslas \times = vector cross-product l = length of wire, measured in meters, vector direction along wire, aligned with positive current.

In the equation above, the current vector I is a vector with magnitude equal to the scalar current, I, and direction pointing along the wire in which the current is flowing.

Alternatively, instead of current, the wire segment l can be considered a vector.

The Lorentz force on a macroscopic current carrier is often referred to as the Laplace force.

Direction of force

The direction of force is determined by the above equations, in particular using the right-hand rule to evaluate the cross product. Equivalently, one can use John Ambrose Fleming's left hand rule for motion, current and polarity to determine the direction of any one of those from the other two, as seen in the example. It can also be remembered in the following way. The digits from the thumb to second finger indicate 'Force', 'B-field', and 'I(Current)' respectively, or F-B-I in short. Another similar trick is the right hand grip rule.

Magnetic field of a steady current .

in a homogenous magnetic field. (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (eg. gravity) (D) In an inhomgeneous magnetic field, grad HThe magnetic field of a steady current (a continual flow of electric charge, for example through a wire, which is constant in time and in which charge is neither building up nor depleting at any point), is described by the Biot-Savart law:

d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \mathbf{\hat r-->{r^2}

(in SI units), where I d\mathbf{l} is a infinitesimal element of current, d\mathbf{B} is the resulting differential contribution to the magnetic field, \mu_0 is the magnetic constant, \mathbf{\hat r} is the unit displacement vector from the current element to the field point, and r is the distance from the current element to the field point.

This is a consequence of Ampere's law, one of the four Maxwell's equations. Alternatively, it can be thought of as a true, empirical law in its own right, which contributes to the derivation of Maxwell's equations. From a practical point of view, though, the law is true and useful regardless of its philosophical origin.

Properties ===Magnetic field lines===

The direction of the magnetic field vector follows from the definition above. It coincides with the direction of orientation of a magnetic dipole, such as a small magnet, or a small loop of current in the magnetic field. So, a cluster of small particles of ferromagnetic material being brought in the magnetic field can be used to show the direction of magnetic field lines (see figure). A trajectory of charged particle (electron Such motion of Solar wind plasma in the magnetic field of Earth results in Northern Lights (and Southern Lights) - spots of glow in upper atmosphere above magnetic poles of Earth where energetic electrons and protons can reach air and ionize nitrogen and oxygen molecules.

Pole labelling confusions See also North Magnetic Pole and South Magnetic Pole.

The end of a compass needle that points north was historically called the "north" magnetic pole of the needle. Since dipoles are vector (spatial) and align "head to tail" with each other to minimize their magnetic potential energy, the magnetic pole located near the geographic North Pole is actually the "south" pole.

The "north" and "south" poles of a magnet or a magnetic dipole are labelled similarly to north and south poles of a compass needle. Near the north pole of a bar or a cylinder magnet, the magnetic field vector is directed out of the magnet; near the south pole, into the magnet. This magnetic field continues inside the magnet (so there are no actual "poles" anywhere inside or outside of a magnet where the field stops or starts). Breaking a magnet in half does not separate the poles but produces two magnets with two poles each.

Earth's magnetic field is probably produced by electric currents in its liquid core.

Rotating magnetic fields The rotating magnetic field is a key principle in the operation of electric motor#AC motorss. A permanent magnet in such a field will rotate so as to maintain its alignment with the external field. This effect was conceptualized by Nikola Tesla, and later utilised in his, and others, early AC (alternating-current) electric motors. A rotating magnetic field can be constructed using two orthogonal coils with 90 degrees phase difference in their AC currents. However, in practice such a system would be supplied through a three-wire arrangement with unequal currents. This inequality would cause serious problems in standardization of the conductor size and so, in order to overcome it, three-phase systems are used where the three currents are equal in magnitude and have 120 degrees phase difference. Three similar coils having mutual geometrical angles of 120 degrees will create the rotating magnetic field in this case. The ability of the three-phase system to create a rotating field, utilized in electric motors, is one of the main reasons why three-phase systems dominate the world's electrical power supply systems.

Because magnets degrade with time, synchronous motors and induction motors use short-circuited Rotor (electric)s (instead of a magnet) following the rotating magnetic field of a multicoiled stator. The short-circuited turns of the rotor develop eddy currents in the rotating field of the stator, and these currents in turn move the rotor by the Lorentz force.

In 1882, Nikola Tesla identified the concept of the rotating magnetic field. In 1885, Galileo Ferraris independently researched the concept. In 1888, Tesla gained for his work. Also in 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin.

Hall effect Because the Lorentz force is charge-sign-dependent (see above), it results in charge separation when a conductor with current is placed in a transverse magnetic field, with a buildup of opposite charges on two opposite sides of conductor in the direction normal to the magnetic field, and the potential difference between these sides can be measured.

The Hall effect is often used to measure the magnitude of a magnetic field as well as to find the sign of the dominant charge carriers in semiconductors (negative electrons or positive holes).

Special relativity and electromagnetism According to special relativity, electric and magnetic forces are part of a single physical phenomenon, electromagnetism; an electric force perceived by one observer will be perceived by another observer in a different frame of reference as a mixture of electric and magnetic forces. A magnetic force can be considered as simply the relativistic part of an electric force when the latter is seen by a moving observer.

More specifically, rather than treating the electric and magnetic fields as separate fields, special relativity shows that they naturally mix together into a rank-2 tensor, called the electromagnetic tensor. This is analogous to the way that special relativity "mixes" space and time into spacetime, and mass, momentum and energy into four-momentum.

Magnetic field shapes descriptions ("four-pole") magnetic field. There are four steel pole tips, two opposing magnetic north poles and two opposing magnetic south poles.

An azimuthal magnetic field is one that runs east-west.
A meridional magnetic field is one that runs north-south. In the solar dynamo model of the Sun, differential rotation of the solar plasma causes the meridional magnetic field to stretch into an azimuthal magnetic field, a process called the omega-effect. The reverse process is called the alpha-effect. The Solar Dynamo, retrieved Sep 15, 2007.
A radial magnetic field is one seen around a straight wire carrying a current. The magnetic field strength decreases with the square of the radial distance from the wire.
A dipole magnetic field is one seen around a charged particle, or around a bar magnetic.
A quadruple magnetic field is one seen between two sets (ie four) bar magnets poles. The quadrupole magnet field strength grows linearly with the radial distance from its longitudinal axis.
A solenoidal magnetic field is similar to a dipole magnetic field, except that a solid bar magnetic is replaces by a hollow electromagnetic coil magnet.
A toroidal magnetic field occurs in a doughnut-shaped coil, the electric current spiraling around the tube-like surface, and is found, for example, in a tokamak.
A poloidal magnetic field is generated by a current flowing in a ring, and is found, for example, in a tokamak.